The integration of generative AI in digital health tools introduces opportunities and challenges to assist healthcare practices and improve health outcomes. A rapid review was performed to investigate the user experience of generative AI in digital health after the introduction of ChatGPT in 2022. Ten papers were included in the review. Findings show three types of generative AI systems (ChatGPT-specific, tailored, and custom) that were developed and studied on user experiences, measurements and outcomes differed between studies, and novel future research directives are needed to ensure good user experiences, trust, and effectiveness of generative AI in digital health.